Versatile analysis of limited plasticity by body force method

A problem of thermally-induced residual stress under plane strain constraint is considered based on a Body Force Method (BFM). As a numerical example, a simple problem of limited plasticity due to a uniform strength of transient line heat source of finite width, which is applied to a surface of a semi-infinite solid for a short duration of time, was considered. Although the out-of-plane component of normal stress (σzz) can be simply estimated from the in-plane normal stress components σxx, σyy and the Poisson’s ratio ν as σzz = ν(σxx + σyy) for elastic plane strain problems, this relation violated when plasticity is considered. As a result, the residual stress in the direction of out-of-plane found to be a major component in the present problem.